Communication systems have evolved over the years to utilize numerous modulation techniques for modulating a carrier. They usually range from amplitude modulation to frequency and phase modulation. For digital systems, some of the more widely used modulation techniques are phase-shift key (PSK) and frequency shift key (FSK) and variations thereof. The selection of the appropriate modulation scheme is a function of a number of factors such as bandwidth, signal to noise ratio and data rate.
In communication systems where a large number of channels are utilized, it is necessary that each channel have a defined bandwidth and that data in one channel does not interfere with data in an adjacent channel (i.e., adjacent channel interference). Therefore, the modulation scheme utilized in this type of system would be influenced by the bandwidth constraints and the required signal to noise ratio of the system in addition to other factors. However, it is imperative that the sidebands of the modulated carrier be confined within the bandwidth of the channel in order to reduce the adjacent channel interference. Such systems as quadrature phase shift key (QPSK) and offset quadrature phase key (XQPSK) have been devised to reduce intersymbol interference and jitter that results from the filtering required for multi-channel systems. In addition, constant envelope modulation schemes such as tamed frequency modulation (TFM) and correlative phase-shift key (CORPSK) have been proposed. These systems provide smooth phase transitions which consequently improve spectral efficiency.
Another method of improving spectral efficiency is cross-correlated phase-shift key (XPSK) which is described in Feher, "IEEE Transactions on Communications", Vol. Com-31, No. 5, May 1983, pp. 702-707. In this system, the two quadrature channels are cross-correlated to smooth the transition from one phase point to another. The XPSK system utilizes a number of predetermined waveform segments to synthesize the quadrature signals. By examining the data stream, a determination can be made as to the conditions necessary for cross-correlation and the appropriate waveform segment to output to a linear modulator. The linear modulator modulates a carrier with the snythesized cross-correlated quadrature waveforms and outputs the modulated carrier to the system. The waveform synthesis is described in U.S. Pat. No. 4,339,724, issued to Feher on July 13, 1982. This system utilizes a group of waveform generators which are multiplexed in time to take particular segments of those waveforms and combine them to output a filter function. However, this system is difficult to implement and the waveform segments are limited to the functions that can be generated.